I believe most people enjoy to idea that ship designs in GC have roles, and that those roles matter. Coming from the "rabid ship designer club" so to speak... I've spent about 2600 hours designing multi-role fighters, vs bombers, vs destroyers, vs siege ships, vs transports, vs bulk landers, vs dropships, vs drop pods, vs battleships, vs battlecruisers... etc. etc. etc.
All for it... to be largely meaningless in game. Ultimately, aside from some edge cases, you just build swarms of the largest ship possible in GC3 (and usually stick to one weapon type, and generally don't bother with thinking about defenses, or abuse the role system/etc.).
I'd really like to see that changed. However, knowing that "tactical combat" is very contentious topic, I'm going to constrain myself to working within the idea, that combat is unchanged from GC3... you move ships, they battle, it's about stats... you move on.
So what do I want to see?
Movement related Specialization
First and foremost, the use of sectors and 'subspace' allows us to differentiate between "Sector only" and "Inter-Sector" travel. I suggest three engine stats on all ships.
Subspace Speed (Inter-Sector Transition Speed)
Sector Speed (Interior Hex Map Movement)
Maneuverability (Special stat that contributes to evasion, but it's contribution to evasion cannot be countered by ECM ECCM/etc. components). Smaller ships get larger Maneuverability bonuses. This bonus for smaller ships is further increased if a battle is occurring "in orbit" of a planet.
Following this guideline, we have already have some important distinct roles in our navy.
1) Strategic Assault: Ships that can go to any sector, fight anywhere... invade the galaxy! (these naturally lend themselves to larger hulls because of the need for larger engines/more engines, they can be countered by smaller hulls, who have some defensive advantages if designed correctly.)
2) Sector Defense: Early game, these are Strategic Assault, but just locally in the sector, by mid-game, these are efficient and cheaper designs that have better arsenals or in-sector speed, because you saved space/money by ignoring Subspace Drives.
3) Orbital Defenders: Ships that are small, eschew good Sector Speed, and generally garrison a planet's "orbit". These ships would have a natural maneuverability bonus, enhanced by staying in orbit, making them "hit above their weight class" in defense.
4) Specialized Orbital Assault: By virtue of #3, late game navies may employ fairly large ships (Cruisers) that focus on boosting maneuverability in order to counter #3 Orbital Defenders, while still travelling strategically. This group would also contain Carriers because of their fighters.
Okay, that's movement, how about some miscellaneous stuff.
Evasion, as mentioned, would be partially dependent on Maneuverability. Additionally a ship can increase evasion by using ECM components. Scanners would help counter this.
Speaking of scanners, most ship scanners should only impact Fog of War within a Sector... while large facilities like Starbases or Planets might reveal information on nearby adjacent Sectors (if at all). I could see extremely specialized Ships doing this as well... but that seems outside of the design intent of previous GC games. I think it's fine that we rely on "facilities" and espionage for Sector info where we have no actual ships/Starbases.
Also, scanner range on the hex-map of a sector should be related to the SUM of all Scanners in a fleet, not merely the longest range of a single vessel. This represents that larger fleets will always have a decent scanner range because they "Spread out". Furthermore, this encourages at least some scanners on most ships, in order to counter enemy evasion as well as contribute to fleet awareness. Special modules to enhance the entire fleet's capabilities can then exist for specialized fleet-boosting vessels.
Transports... as has been suggested by Frogboy... he's thinking every ship in a fleet will have a natural contribution to ground assault, while Transports will obviously contribute massively. Allowing fleets without transports to overtake minor colonies of likely thousands of civilians.... but requiring Transports to invade major homeworlds and the like. I personally like this. I would merely amend, that Carriers should provide a ground assault bonus, surpassing other ships in their weight class, as they provide "air support".
Speaking of Carriers... there are many ways to treat these... however, I think given GCIII's overall design... it would have been better to have Carriers be a ship that boosts various stats for Tiny and Small ships... rather than deploying Tiny ships as a weapon system. I also am perfectly fine with Fighters being a sub-Tiny class ship, that follows it's own special rules and is added to our Rock/Paper/Scissors of weapons design. But if Fighters are just Tiny Ships... then Tiny Ships should be added to a fleet, and Carriers should boost their Sector-Speed to the Carrier's Sector Speed, and give a variety of repair/etc. bonuses.
If on the other hand Fighters are a new weapon system, that isn't necessarily treated as "kinetic/Beam/missile" but is it's own category... Cool. I'm very cool with that.
Ultimately, size of ship hull should interact with Maneuverability and Tracking to punish engagements between unbalanced fleets, with an advantage given to Tiny Hulls in purely defensive engagements (orbit).
Weapons and Defenses and Targeting Priorities
There's many ways to skin a cat, and there are many ways to design weapons. I'm less picky about this subject in how they interact with defenses on a mathematic level. However, I can see some unique elements opened up by virtue of my notes above, that would allow for interesting specializations.
Missiles should arguably be short-ranged weapons (and if ship's had "supplies" in GCIV then they should exhaust quickly), but the missile itself is Maneuverable. Missile Weapons should therefore be the best weapon system to use against Tiny/Small ships and Fighters, especially ones in Orbital Defense battles. If supply is a factor, missile based ships would be poor for ships intended to operate offensively for long periods of time. This could be abstracted to increased fire rates when being used in orbit I suppose (constant resupply).
Kinetics could give a fleet a modest bombardment/ground assault bonus (Beams diffuse in atmosphere, and missiles can be countered by point defense).
Beams/Other Energy Weapons could be very high damaging, accurate, and long ranged, in general, they could just outclass other weapons... but they could have downsides... specifically a low rate of fire, and "heating up" the firing ship, and reducing its Evasion score as a result. Essentially... it is a big hot target compared to other ships and is more easily tracked. Beams could also have bonuses or disadvantages in Nebulas due to their energy interacting with the gasses of the nebula.
Point Defense occupies an odd place, where, if fighters become a weapon system, then Point Defense should arguably work against them, making it a 2 for 1 defense system. You could also make the case, that Point Defense systems should be able to "attack" Tiny Hull ships, if said Tiny Hulls are "Fighters". It's an odd duck. I personally think PD should work against Fighters, but some versions of it are specifically better than others. So, "Chaff" works against missiles but really doesn't against Fighters, and others are more balanced in anti-missile and anti-fighter capabilities.
Component Slots need to be Specialized as well... no matter how much you try, if you can always use every slot for a weapon, it's likely to mean that the only "valid" designs are all weapons and engines. Having slots for Weapons or Defenses, and slots for Engines and slots for "Special equipment" forces this problem into submission. If you have a more clever way than that... great.
There's more to discuss about targeting priorities and how ship speed and behavior should work, and how weapons and defenses should interact, but I'll leave that to more math-happy friends for now. Suffice to say, I think shields and armor should assist against all weapons to a degree... and a All Battleship Fleet should be absolutely trounced by larger numbers of Tiny ships or Carriers, at least in Orbit.
So, I think if the above were all applied... you'd get some very interesting specialization going. Which maybe wouldn't matter to most player empires playing on easy difficulties and economically dominating already... but player's who are facing an uphill battle could really take advantage of.
Tiny and Small ships armed with missiles ought to perform amazingly in planetary defense... and would be favored by those Minor Race planets that are resisting your armada... you'd still blow them over, but you'd suffer more than you'd expect and it would slow your march to conquest. You could avoid this by using Carriers who'd assist in the ground battle afterwards... and those Kinetic bearing battleships would also help.
Meanwhile, your defense fleets in important sectors with industrial capacity have to be outnumbered to be taken down because they eschew Subspace drives and pack additional weapons and defenses, maybe focusing on Beams for sheer power, even if it means they take a few more losses due to the evasion loss (they are afterall in home turf where they can be replaced faster).
Evasion and counter evasion mechanics should generally force any fleet to maintain a solid number of Medium hulls to protect their larger vessels from those swarms of enemy Tiny hulls... And a single small ship alone in a sector just isn't going to see very much. But a fleet will and can become omniscient with the right fleet-booster ship.
Finally... if a player just can't be bothered? Then they just mass produce Medium hulls sprinkle in some Large/Huge, and they should do pretty well.
Regardless of any of the details I'm suggesting... that's the sort of design I want to see in GCIV ships, and it's really all to do with stats and their interaction. Hopefully this was all pretty cogent.